A new construction of Lagrangians in the complex Euclidean plane in terms of planar curves

We introduce a new method to construct a large family of Lagrangian surfaces in complex Euclidean plane by means of two planar curves making use of their usual product as complex functions and integrating the Hermitian product of their position and tangent vectors. Among this family, we characterize minimal, constant mean curvature, Hamiltonian stationary, solitons for mean curvature flow and Willmore surfaces in terms of simple properties of the curvatures of the generating curves. As an application, we provide explicitly conformal parametrizations of known and new examples of these classes of Lagrangians in complex Euclidean plane.Comment: 15 pages, 5 figure

Quantitative Analysis of the Effective Functional Structure in Yeast Glycolysis

Yeast glycolysis is considered the prototype of dissipative biochemical oscillators. In cellular conditions, under sinusoidal source of glucose, the activity of glycolytic enzymes can display either periodic, quasiperiodic or chaotic behavior. In order to quantify the functional connectivity for the glycolytic enzymes in dissipative conditions we have analyzed different catalytic patterns using the non-linear statistical tool of Transfer Entropy. The data were obtained by means of a yeast glycolytic model formed by three delay differential equations where the enzymatic speed functions of the irreversible stages have been explicitly considered. These enzymatic activity functions were previously modeled and tested experimentally by other different groups. In agreement with experimental conditions, the studied time series corresponded to a quasi-periodic route to chaos. The results of the analysis are three-fold: first, in addition to the classical topological structure characterized by the specific location of enzymes, substrates, products and feedback regulatory metabolites, an effective functional structure emerges in the modeled glycolytic system, which is dynamical and characterized by notable variations of the functional interactions. Second, the dynamical structure exhibits a metabolic invariant which constrains the functional attributes of the enzymes. Finally, in accordance with the classical biochemical studies, our numerical analysis reveals in a quantitative manner that the enzyme phosphofructokinase is the key-core of the metabolic system, behaving for all conditions as the main source of the effective causal flows in yeast glycolysis.Comment: Biologically improve

Approach to the chronology of the cave necropolis of "Las Cuevas" (Osuna, Sevilla): The caves 5 and 6

Del análisis combinado de los datos que nos han ofrecido las excavaciones arqueológicas que se llevaron a cabo en 1985 en las cuevas 5 y 6, y los recogidos en intervenciones anteriores, practicadas desde el siglo XVI, pretendemos realizar una caracterización de la necrópolis de la Vereda Real de Granada o de Las Cuevas (Osuna, Sevilla).Our aim in this paper is to characterize the late-roman necropolis of Vereda Real de Granada, known as well as “Las Cuevas” (Osuna, Sevilla). For this, we use the combined analysis of the data recovered not only from the excavations carried out in 1985 in caves 5 and 6 but also from earlier fieldworks since XVI century.España. Ministerio de Ciencia y Tecnología BHA2003- 08652Junta de Andalucí

Half-space Gaussian symmetrization: applications to semilinear elliptic problems

Abstract We consider a class of semilinear equations with an absorption nonlinear zero order term of power type, where elliptic condition is given in terms of Gauss measure. In the case of the superlinear equation we introduce a suitable definition of solutions in order to prove the existence and uniqueness of a solution in ℝ N without growth restrictions at infinity. A comparison result in terms of the half-space Gaussian symmetrized problem is also proved. As an application, we give some estimates in measure of the growth of the solution near the boundary of its support for sublinear equations. Finally we generalize our results to problems with a nonlinear zero order term not necessary of power type

Self-interacting dipolar boson stars and their dynamics

We construct and dynamically evolve dipolar, self-interacting scalar boson stars in a model with sextic (+ quartic) self-interactions. The domain of existence of such dipolar $Q$-stars has a similar structure to that of the fundamental monopolar stars of the same model. For the latter it is structured in a Newtonian plus a relativistic branch, wherein perturbatively stable solutions exist, connected by a middle unstable branch. Our evolutions support similar dynamical properties of the dipolar $Q$-stars that: 1) in the Newtonian and relativistic branches are dynamically robust over time scales longer than those for which dipolar stars without self-interactions are seen to decay; 2) in the middle branch migrate to either the Newtonian or the relativistic branch; 3) beyond the relativistic branch decay to black holes. Overall, these results strengthen the observation, seen in other contexts, that self-interactions can mitigate dynamical instabilities of scalar boson star models.Comment: 13 pages, 14 figures; movies of the numerical simulations reported can be found in http://gravitation.web.ua.pt/index.php/node/448

The Clifford torus as a self-shrinker for the Lagrangian mean curvature flow

We provide several rigidity results for the Clifford torus in the class of compact self-shrinkers for Lagrangian mean curvature flow.Comment: 10 page